Ambiguity Resolution and Localization Method Based on Double-Difference Phase Observation

Abstract

This invention relates to an ambiguity resolution and positioning method based on double-difference phase observation, belonging to the field of wireless positioning technology. The method includes the following steps: S1: Selecting the frequency range of signal transmission and calculating the wavelength corresponding to each frequency point; S2: Introducing noise to generate simulated observation values; S3: Constructing the double-difference phase observation equation; S4: Calculating the floating-point solution using the weighted least squares method; S5: Fixing the integer ambiguity solution and optimizing the position parameters; S6: Comparing the phase changes of the target object at continuous time points and calculating the actual displacement value. This invention reduces the complexity of ambiguity resolution and improves computational efficiency; enhances noise robustness and improves positioning accuracy in complex environments; optimizes the double-difference design matrix and improves system stability; improves positioning accuracy, achieving a centimeter-level error range; and has the potential to be extended to adapt to 5G NR scenarios.

Description

Technical Field

[0001] This invention belongs to the field of wireless positioning technology and relates to an ambiguity resolution and positioning method based on double-difference phase observation. Background Technology

[0002] Wireless positioning technology is a crucial component of modern communication and navigation, widely applied in Global Navigation Satellite Systems (GNSS), Indoor Positioning Systems (IPS), and high-precision positioning systems based on 5G New Radio (5GNR) signals. With continuous technological advancements, positioning methods are evolving from traditional Time of Arrival (TOF) and Received Signal Strength (RSS) measurements to high-precision ranging based on carrier phase observation. In GNSS, carrier phase observation, with its short wavelength and high accuracy, has become a core technology for achieving centimeter-level accuracy. For example, Real-Time Kinematic (RTK) eliminates system errors through double-difference observations, achieving centimeter-level accuracy. For indoor positioning, due to significant multipath effects, traditional TOF and RSS methods struggle to meet high-precision requirements, making multi-frequency carrier phase observation a research hotspot for achieving sub-meter or centimeter-level positioning. However, challenges remain, such as the high complexity of ambiguity resolution in complex environments and the susceptibility of the observation matrix to noise. More efficient and robust solutions are urgently needed.

[0003] Currently, in high-precision positioning technology, ambiguity resolution of carrier phase observation is a key step in achieving high accuracy. Existing technical solutions mainly include the following methods. Teunissen PJG proposed an integer ambiguity resolution method in his conference paper "Least-square sestimation of the integer GPS ambiguities." By performing decorrelation processing on the ambiguity parameters, he improved the success rate of fixing integer ambiguities. After its widespread adoption, this method was named the LAMBDA method. Vollath U et al. proposed a Three-Carrier Ambiguity Resolution (TCAR) method in the journal "Analysis of Three-Carrier Ambiguity Resolution Technique for Precise Relative Positioning in GNSS-2". This method utilizes a combination of multi-frequency observations to progressively fix ambiguities at the ultra-wide lane, wide lane, and narrow lane levels, achieving rapid resolution. With the evolution of GNSS integer ambiguity resolution techniques, the Cascade Integer Resolution (CIR) method has also been widely applied in multi-frequency GNSS relative positioning technology. Based on integer-guided estimation criteria, it progressively fixes ambiguities, and its algorithm is simple to implement and has a high success rate. In the following years, researchers gradually realized the limitations of the LAMBDA algorithm in certain complex situations. To overcome these shortcomings, the MLAMBDA method emerged, further improving the accuracy and reliability of ambiguity resolution by introducing techniques such as maximum likelihood estimation. While these methods have achieved significant results in certain scenarios, there is still room for improvement in areas such as ambiguity resolution complexity, noise robustness, and matrix rank optimization. First, traditional ambiguity resolution methods are complex in high-dimensional, multi-frequency scenarios, making it difficult to meet real-time requirements. Second, the double-difference design matrix is ​​prone to insufficient rank when the frequency or location points are improperly distributed, leading to unstable results. Furthermore, existing technologies are not fully adapted to complex scenarios (such as 5G positioning and indoor positioning), resulting in unstable positioning performance or insufficient accuracy. These problems severely restrict the practical application of high-precision positioning technology in complex scenarios. Summary of the Invention

[0004] In view of this, the purpose of this invention is to address the problems of high ambiguity resolution complexity, insufficient rank of the double-difference design matrix, and significant impact of noise interference on positioning accuracy in existing high-precision positioning technologies. To propose an efficient ambiguity resolution and positioning method based on double-difference phase observation, this invention combines weighted least squares, an optimized MLAMBDA method, and weighted processing of the noise covariance matrix to achieve high-precision positioning in complex scenarios.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for ambiguity resolution and localization based on double-difference phase observation includes the following steps:

[0007] S1: Select the frequency range for signal transmission and calculate the wavelength corresponding to each frequency point;

[0008] S2: Introduce noise to generate simulated observations;

[0009] S3: Construct the double-difference phase observation equation;

[0010] S4: Calculate the floating-point solution using the weighted least squares method;

[0011] S5: Fixed integer ambiguity solution, optimizing position parameters;

[0012] S6: Compare the phase changes of the target object at consecutive time points and calculate the actual value of the displacement.

[0013] Further, in step S1, 2.8GHz to 2.89GHz is selected as the frequency range for signal transmission, the transmission frequency step size is set, and the frequency points are distributed at equal intervals to generate a frequency list; the wavelength corresponding to each frequency point is calculated one by one using the following formula, and the results are stored in the wavelength list;

[0014]

[0015] in Let c be the frequency of the j-th frequency point, and c be the speed of light. Let be the wavelength corresponding to the j-th frequency.

[0016] Furthermore, step S2 specifically includes the following steps:

[0017] Define the initial distance and the distance after each movement, and generate a list of distances;

[0018] Add the initial distance to the beginning of the distance list;

[0019] Read the number of positions (num_positions) and the number of frequencies (num_frequencies);

[0020] Initialize the phase matrix and define the noise level;

[0021] The system iterates through each target location and frequency point. For location i and frequency j, the theoretical phase value between the target and the receiver is calculated using the carrier phase formula, which is:

[0022]

[0023] in This represents the actual distance between the target location i and the receiver. This represents the theoretical phase value at frequency j corresponding to target position i;

[0024] Gaussian noise is then superimposed to simulate the actual observations, and the results are finally restricted to the range of [-π, π] to form a tangled phase.

[0025] Furthermore, step S3, which involves constructing the double-difference phase observation equation, includes the following steps:

[0026] Select a reference frequency and initialize the double-difference phase difference. and design matrix A dd With G dd For all adjacent position pairs, first calculate the phase difference between adjacent positions i and i+1 at different frequencies, i.e.:

[0027]

[0028] This represents the theoretical phase value at position i corresponding to frequency j. This represents the theoretical phase value at frequency j corresponding to position i+1. Let represent the phase difference between positions i and i+1 at frequency j. Wrap the phase difference to confine it to the range [-π, π]. Then calculate the reference frequency phase difference between adjacent positions i and i+1:

[0029]

[0030] This represents the phase value of the reference frequency at position i. This represents the phase value of the reference frequency at position i+1; This represents the phase difference between positions i and i+1 at the reference frequency; using the reference frequency as the reference frequency, iterate through all frequency points except the reference frequency one by one, and calculate the double-difference phase difference corresponding to the reference frequency. :

[0031]

[0032] This represents the phase difference between positions i and i+1 at frequency j. This represents the phase difference between positions i and i+1 at the reference frequency. That is, the double-difference phase difference at position i;

[0033] Constructing the double-difference design matrix A dd This is used to record the wavenumber difference information for each frequency; an integer design matrix G is constructed. dd Used to record the integer ambiguity between each frequency and position; where each G dd The elements in the matrix are assigned the value 2π, representing the unit contribution of integer ambiguity. Used to skip the reference frequency and ensure that only the ambiguity contribution of non-reference frequencies is recorded in the matrix, as shown below:

[0034]

[0035]

[0036] The double-difference phase difference calculated each time This will be used to fill the double-difference phase difference vector, while updating the double-difference design matrix and the integer design matrix.

[0037] Furthermore, step S4 specifically includes the following steps:

[0038] Construct the noise covariance matrix Q y_dd With overall design matrix D dd According to the principle of noise superposition:

[0039]

[0040]

[0041]

[0042] The standard deviation of single-difference observation noise is represented. Let I represent the variance of the double-difference observation noise, and I be the identity matrix.

[0043] Check the condition number and rank of the design matrix; if the condition number is greater than 10... 12 If the rank is less than the number of columns in the matrix, it means that the matrix is ​​not full rank and cannot be inverted or pseudo-inverse, which may result in a non-unique solution or no solution at all.

[0044] The floating-point solution of the double-difference equation, including the position change parameters, is calculated using the pseudo-inverse. and ambiguity parameters The preliminary estimate is expressed as:

[0045]

[0046]

[0047]

[0048]

[0049] The overall design matrix contains the linear relationship between the double-difference phase difference and the parameters, Q. y_dd The noise covariance matrix is... It is a double-difference phase difference. The estimated parameter vector includes position change parameters and ambiguity parameters; For position change parameters, For ambiguity parameters;

[0050] Extracting the covariance matrix of integer ambiguities For subsequent accuracy analysis:

[0051]

[0052]

[0053] This is the complete parametric covariance matrix, containing the covariance of position parameters and integer ambiguities; is the covariance matrix of the integer ambiguity portion.

[0054] Furthermore, step S5 specifically includes the following steps:

[0055] Based on floating-point fuzzy solution An improved MLAMBDA method is used to fix integer ambiguities. For the ambiguity covariance matrix Perform LDL T Decomposition yields the solution-related transformation matrix Z, the lower triangular matrix L, and the diagonal matrix D. The floating-point ambiguity is then resolved through transformation. Transform to the new coordinate system As shown in the following formula:

[0056]

[0057]

[0058] Based on the ambiguity parameters after uncorrelation By using the least squares criterion to perform an integer search, the fixed integer fuzzy solution is finally determined. :

[0059]

[0060] Fixed integer fuzzy solution Mapping back to the original coordinate system yields the final integer ambiguity solution. :

[0061]

[0062] Re-estimation of position change parameters using weighted least squares method :

[0063]

[0064] .

[0065] The beneficial effects of this invention are as follows:

[0066] 1. Reduce the complexity of ambiguity resolution and improve computational efficiency.

[0067] The invention employs a weighted least squares method combined with pseudo-inverse matrix solving, significantly reducing the computational complexity of ambiguity resolution. Compared to traditional direct inversion methods, it maintains stable computational efficiency even as the number of frequency and location points increases.

[0068] 2. Enhance noise robustness and improve positioning accuracy in complex environments.

[0069] By constructing a noise covariance matrix to weight the observations, the ambiguity resolution results in high-noise scenarios are made more stable. Experiments show that this method can effectively suppress noise interference with positioning results and improve positioning accuracy, and is especially suitable for complex indoor scenarios.

[0070] 3. Optimize the double-difference design matrix to improve system stability.

[0071] By constructing a reasonable double-difference observation equation and optimizing the distribution of frequency and location points, the problem of unstable solution caused by insufficient rank of the design matrix was overcome.

[0072] 4. Improve positioning accuracy, achieving centimeter-level error range.

[0073] By combining the optimized fixation of floating-point solutions and integer ambiguities, this invention achieves centimeter-level error range in the estimation of relative distance differences, which is significantly more accurate than the sub-meter-level error of traditional methods.

[0074] 5. Possesses the potential to expand and adapt to 5G NR scenarios.

[0075] The double-difference observation equation and ambiguity resolution process designed in this invention exhibit stable performance in multi-frequency signal scenarios and are compatible with the mid-frequency band of 5G NR. Due to the high tolerance of double-difference observation and weighted least squares method to multi-frequency signals, as well as the high efficiency of ambiguity resolution, it can theoretically be adapted to high-frequency signals and has the potential to be further adapted to high-frequency band signals.

[0076] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0077] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0078] Figure 1 The flowchart shows the ambiguity resolution and localization method based on double-difference phase observation.

[0079] Figure 2 This is a comparison chart of the estimated and actual relative distance differences.

[0080] Figure 3 This is a graph showing the relative distance difference error analysis.

[0081] Figure 4 This is an example diagram illustrating an application scenario. Detailed Implementation

[0082] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0083] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0084] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.

[0085] This embodiment provides a high-precision displacement monitoring scheme based on dual-difference phase observation, suitable for outdoor long-distance scenarios. The scheme aims to accurately monitor minute displacements of buildings or large structures, especially when close-range monitoring is not possible. The selection of a frequency range of 2.8 GHz to 2.89 GHz aims to provide more stable signal quality and higher measurement accuracy through precise phase measurement of high-frequency signals.

[0086] A high-precision displacement monitoring scheme based on dual-difference phase observation is proposed, with the following scenario: monitoring the displacement changes of large structures such as high-rise buildings and bridges under wind loads or other external forces. The distance between the monitoring equipment and the target structure is set to 50 to 100 meters to optimize the quality of signal propagation and reflection.

[0087] like Figure 1 As shown, the steps of the ambiguity resolution and localization method based on double-difference phase observation of the present invention are as follows:

[0088] Step 1: Frequency selection.

[0089] The frequency range of 2.8 GHz to 2.89 GHz was selected as the signal transmission frequency range. This frequency band has good penetration and low atmospheric attenuation, making it suitable for long-distance outdoor transmission and monitoring of target structures in environmental environments. The transmission frequency step size (e.g., 10 MHz) can be set as needed to generate an equally spaced frequency list, ensuring that the signal coverage and frequency resolution meet the requirements. A frequency list of 10 frequency points is generated according to an equally spaced distribution. The wavelength corresponding to each frequency point is calculated using Formula 1, and the results are stored in the wavelength list.

[0090] (1)

[0091] in Let c be the frequency of the j-th frequency point, and c be the speed of light. Let be the wavelength corresponding to the j-th frequency.

[0092] Step 2: Equipment configuration and installation.

[0093] Transmitter: Equipped with a microwave signal transmitter supporting transmission in the 2.8GHz to 2.89GHz frequency band, capable of continuous or frequency-hopping transmission. The transmitter's directional antenna should be pointed towards the monitored target object to ensure signal strength coverage of the target area.

[0094] Receiver: Equipped with a high-sensitivity receiver, the receiver must include a signal demodulation and processing unit capable of receiving and demodulating the phase information in the reflected signal in real time. Simultaneously, the receiver should possess anti-interference capabilities and stability to avoid the impact of environmental changes on measurement accuracy.

[0095] Step 3: Signal debugging and calibration.

[0096] Adjust the transmitter's transmission power and frequency range to ensure the signal covers the target monitoring area. Adjust the receiver's sensitivity and directionality to ensure clear reception of signals reflected from the target.

[0097] Perform preliminary signal calibration: The transmitting and receiving equipment needs to operate in a stable reference environment, collect initial observation data, and use this data to calibrate system parameters (such as initial phase deviation, background noise level, etc.) to provide a benchmark for subsequent data processing.

[0098] Step 4: Double-difference phase observation and data collection.

[0099] First, double-difference phase observation is performed. The transmitting device continuously transmits signals according to a preset frequency list (2.8GHz to 2.89GHz, with a step size of 10MHz). The receiver records the signals reflected back from the target object, continuously collecting phase data of the target object at different frequency points and different position states. Specifically, according to the frequency list, phase information at ten different frequencies is grouped together, and ten groups are taken consecutively (this can be determined by the user). When the position changes, the phase information in the corresponding group at the changed position will change. The data is stored locally or transmitted to a remote data processing center via a wireless network for subsequent analysis.

[0100] Step 5: Data processing and displacement calculation.

[0101] 1. Use data processing software such as MATLAB to demodulate the collected phase data and extract the phase information of the target object at different positions and frequencies. Specifically, this includes:

[0102] Define the initial distance and the distance after each movement, and generate a distance list. Add the initial distance to the beginning of the list. Read the number of positions (num_positions) and the number of frequencies (num_frequencies). Initialize the phase matrix and define the noise level as 0.03 radians. Iterate through each target position and frequency point. For each position i and each frequency j, calculate the theoretical phase value between the target and the receiver using the carrier phase formula (Equation 2):

[0103] (2)

[0104] in This represents the actual distance between the target location i and the receiver. This represents the theoretical phase value at frequency j corresponding to target position i. Gaussian noise is then superimposed to simulate the actual observed value, and finally the result is restricted to the range [-π, π] to form a wrapped phase.

[0105] 2. Construct a double-difference observation equation, record the displacement information of the target object by designing a matrix, and combine the observed values ​​and the noise covariance matrix to calculate the floating-point ambiguity solution using the weighted least squares method; specifically including:

[0106] Select the reference frequency (the first frequency in the frequency list) and initialize the double-difference phase difference. and design matrix A dd With G dd For all adjacent position pairs, first calculate the phase difference between adjacent positions i and i+1 at different frequencies, i.e.

[0107] (3)

[0108] This represents the theoretical phase value at position i corresponding to frequency j. This represents the theoretical phase value at frequency j corresponding to position i+1. Let represent the phase difference between positions i and i+1 at frequency j. Wrap this phase difference to confine it to the range [-π, π]. Then calculate the reference frequency phase difference between adjacent positions i and i+1:

[0109] (4)

[0110] This represents the phase value of the reference frequency at position i. This represents the phase value of the reference frequency at position i+1. This represents the phase difference between positions i and i+1 at the reference frequency. Using the reference frequency as the reference frequency, iterate through all frequency points except the reference frequency and calculate the double-difference phase difference corresponding to the reference frequency. :

[0111] (5)

[0112] This represents the phase difference between positions i and i+1 at frequency j. This represents the phase difference between positions i and i+1 at the reference frequency. That is, the double-difference phase difference at position i. Simultaneously, construct the double-difference design matrix A. dd (This records the wavenumber difference information for each frequency) and the integer design matrix G. dd (Records the integer ambiguity between each frequency and position), where each G dd The elements in the matrix are assigned the value 2π, representing the unit contribution of integer ambiguity. This is used to skip the reference frequency, ensuring that only the ambiguity contribution of non-reference frequencies is recorded in the matrix. See equations 6 and 7:

[0113] (6)

[0114] (7)

[0115] The double-difference phase difference calculated each time This will be used to fill the double-difference phase difference vector, while updating the double-difference design matrix and the integer design matrix, providing support for parameter estimation in subsequent positioning algorithms.

[0116] Construct the noise covariance matrix Q y_dd With overall design matrix D dd According to the principle of noise superposition:

[0117] (8)

[0118] (9)

[0119] (10)

[0120] The standard deviation of single-difference observation noise is represented. Let I represent the variance of the double-difference observation noise, and let I be the identity matrix.

[0121] Check the condition number and rank of the design matrix. If the condition number is large (greater than 10)... 12 If the rank is less than the number of columns in the matrix, it means that the matrix is ​​not full rank and cannot be inverted or pseudo-inverse, which may result in a non-unique solution or no solution at all.

[0122] The floating-point solution of the double-difference equation, including the position change parameters, is calculated using the pseudo-inverse. and ambiguity parameters The preliminary estimate. Equation 12 can be derived from Equation 11; the derivation process will not be elaborated in detail:

[0123] (11)

[0124] (12)

[0125] (13)

[0126] (14)

[0127] The overall design matrix contains the linear relationship between the double-difference phase difference and the parameters, Q. y_dd The noise covariance matrix is... It is a double-difference phase difference. The estimated parameter vector (including position change parameters and ambiguity parameters). For position change parameters, This is the ambiguity parameter.

[0128] Extracting the covariance matrix of integer ambiguities For subsequent accuracy analysis:

[0129] (15)

[0130] (16)

[0131] This is the complete parametric covariance matrix, containing the covariance of position parameters and integer ambiguities. is the covariance matrix of the integer ambiguity portion.

[0132] 3. The ambiguity is fixed using an improved MLAMBDA method to obtain an accurate integer ambiguity solution; finally, displacement calculation is performed, and the displacement parameters are optimized based on the fixed ambiguity solution and the double-difference observation equation; specifically including:

[0133] Based on floating-point fuzzy solution An improved MLAMBDA method is used to fix integer ambiguities. Specifically, regarding the ambiguity covariance matrix... Perform LDL T Decomposition yields the solution-related transformation matrix Z, the lower triangular matrix L, and the diagonal matrix D. The floating-point ambiguity is then resolved through transformation. Transform to the new coordinate system As shown in equations 17 and 18:

[0134] (17)

[0135] (18)

[0136] Based on the ambiguity parameters after uncorrelation By using the least squares criterion to perform an integer search, the fixed integer fuzzy solution is finally determined. :

[0137] (19)

[0138] Fixed integer fuzzy solution Mapping back to the original coordinate system yields the final integer ambiguity solution. :

[0139] (20)

[0140] Re-estimation of position change parameters using weighted least squares method :

[0141] (twenty one)

[0142] (twenty two)

[0143] Compare the phase changes of the target object at consecutive time points and calculate the actual value of the displacement.

[0144] Step 6: Data Output and Application.

[0145] like Figure 2-3 As shown, a graphical user interface is used to display real-time monitoring data, including the displacement trend and current status of the target object. Important time points or abnormal change points are marked on the charts to facilitate the identification of key data by monitoring personnel. Historical displacement data during the monitoring period is compiled to generate a trend analysis report. The report should include displacement change curves, amplitude statistics, and an analysis of the impact of environmental factors (such as wind speed, temperature changes, etc.). Displacement thresholds are set according to actual needs. When the target displacement value exceeds the set threshold, the alarm system is automatically triggered, notifying monitoring personnel to take timely measures via audible and visual signals or SMS.

[0146] Step 7: Monitoring and maintenance.

[0147] Regularly check the operational status of transmitting and receiving equipment to ensure stable signal transmission and reception. Calibrate equipment parameters to adapt to changes in the external environment (such as the effects of temperature and humidity on the signal). If abnormal data is detected, inspect and replace potentially faulty equipment components (such as antennas or signal processing units); regularly clean equipment surfaces to prevent dust or debris from obstructing the signal propagation path. Application scenarios include... Figure 4 As shown.

[0148] In the above embodiments, the reference to "this embodiment" in the specification indicates that a specific feature, structure, or characteristic described in connection with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple appearances of "this embodiment" do not necessarily refer to the same embodiment.

[0149] In the above embodiments, although the invention has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory structures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed. The embodiments of the invention are intended to cover all such substitutions, modifications, and variations falling within the broad scope of the appended claims.

[0150] This embodiment also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the methods in this embodiment.

[0151] This embodiment also provides an electronic terminal, including: a processor and a memory;

[0152] The memory is used to store computer programs, and the processor is used to execute the computer programs stored in the memory to cause the terminal to perform any of the methods in this embodiment.

[0153] As will be understood by those skilled in the art, the computer-readable storage medium described in this embodiment allows for the implementation of all or part of the steps in the above method embodiments by computer program-related hardware. The aforementioned computer program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0154] The electronic terminal provided in this embodiment includes a processor, a memory, a transceiver, and a communication interface. The memory and the communication interface are connected to the processor and the transceiver and complete communication between them. The memory is used to store computer programs, the communication interface is used to perform communication, and the processor and the transceiver are used to run the computer programs, so that the electronic terminal performs the steps of the above method.

[0155] In this embodiment, the memory may include random access memory (RAM) and may also include non-volatile memory, such as at least one disk storage device.

[0156] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0157] This invention can be used in a wide range of general-purpose or special-purpose computing system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.

[0158] This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform a specific task or implement a specific abstract data type. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0159] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for ambiguity resolution and positioning based on double-difference phase observations, characterized in that: The method comprises the following steps: S1: selecting a frequency range of signal transmission, calculating the wavelength corresponding to each frequency point; S2: introducing noise to generate simulated observations; S3: constructing double-difference phase observation equations; S4: calculating a floating-point solution by using a weighted least squares method; S5: fixing an integer ambiguity solution and optimizing position parameters; S6: comparing the phase changes of the target object at consecutive time points to calculate the actual value of displacement.

2. The double-difference phase observation based ambiguity resolution and positioning method according to claim 1, characterized in that: In step S1, 2.8 GHz to 2.89 GHz is selected as the frequency range of signal transmission, the transmission frequency step is set, the frequency points are generated in an equidistant distribution to form a frequency list, the wavelength corresponding to each frequency point is calculated by using the following formula, and the result is stored in a wavelength list. wherein is the frequency of the jth frequency point, c is the speed of light, is the wavelength corresponding to the jth frequency.

3. The double-difference phase observation based ambiguity resolution and positioning method according to claim 1, wherein: Step S2 specifically comprises the following steps: Defining an initial distance and a distance after each move to generate a distance list; Adding the initial distance to the beginning of the distance list; Reading the number of positions num_positions and the number of frequency points num_frequencies; Initializing a phase matrix and defining a noise level; Iterating through each target position and frequency point, for position i and frequency j, calculating the theoretical phase value between the target and the receiver by using a carrier phase formula, wherein the carrier phase formula is: wherein represents the actual distance between the target position i and the receiver, represents the theoretical phase value for the corresponding frequency j at the target position i; Superimposing Gaussian noise to simulate actual observations, and finally limiting the result to the range of [-π, π] to form a wrapped phase.

4. The double-difference phase observation based ambiguity resolution and positioning method according to claim 1, wherein: Step S3 of constructing double-difference phase observation equations comprises the following steps: Selecting a reference frequency, initializing the double-difference phase difference and design matrix A dd with G dd ; for all pairs of adjacent positions, first calculate the phase difference at different frequencies between adjacent positions i and i+1, that is: represents the theoretical phase value for frequency j at position i, represents the theoretical phase value for frequency j at position i+1, represents the phase difference between positions i and i+1 at frequency j, the phase difference is wrapped, limited to the range [-π, π]; the reference frequency phase difference between adjacent positions i and i+1 is calculated: represents a phase value of the reference frequency at position i, represents a phase value of the reference frequency at position i+1; represents a phase difference between positions i and i+1 at the reference frequency; all frequency points other than the reference frequency are traversed one by one, and a double-difference phase difference corresponding to the reference frequency is calculated : denotes the phase difference between positions i and i+1 at frequency j, denotes the phase difference between positions i and i+1 at the reference frequency, i.e. the double-difference phase difference for position i; Constructing double-difference design matrix A dd for recording the wave number difference information of each frequency; constructing integer design matrix G dd for recording the integer ambiguity between each frequency and position; wherein each element in G dd matrix is assigned a value of 2π, representing the unit contribution of integer ambiguity, to skip the reference frequency, ensuring that only the ambiguity contribution of non-reference frequency is recorded in the matrix, as shown below: double-difference phase differences filling the double-difference phase difference vector while updating the double-difference design matrix and the integer design matrix.

5. The double-difference phase observation based ambiguity resolution and positioning method according to claim 1, characterized in that: Step S4 Specifically comprising the following steps: Constructing the noise covariance matrix Q y_dd with the total design matrix D dd According to the noise superposition principle, we have: σ0represents a standard deviation of single-difference observation noise, σ1represents a variance of double-difference observation noise, I is an identity matrix; Check the condition number and rank of the design matrix, if the condition number is greater than 10 12 , it means that the matrix is close to singular, which may lead to numerical instability; if the rank is less than the number of columns of the matrix, it means that the design matrix is not full rank, which cannot be operated by inverse or pseudo-inverse calculation, which may lead to non-unique solution or cannot be solved; A float solution of the double difference equations is computed using the pseudo-inverse, including initial estimates of the position change parameters and ambiguity parameters denoted by is the total design matrix, containing the linear relationship between double-difference phase differences and parameters, Q y_dd is the noise covariance matrix, is the double-difference phase difference, is the estimated parameter vector, including the position change parameter and the ambiguity parameter; is the position change parameter, is the ambiguity parameter; Extracting integer ambiguities covariance matrix For subsequent accuracy analysis: Covariance matrix for the complete parameter, containing the position parameters and the integer ambiguities; Covariance matrix for the integer ambiguity part.

6. The double-difference phase observation based ambiguity resolution and positioning method according to claim 1, wherein: Step S5 specifically comprises the following steps: Integer ambiguity resolution based on float ambiguity solutions using an improved MLAMBDA method LDL decomposition of the ambiguity covariance matrix T to obtain an uncorrelated transformation matrix Z, a lower triangular matrix L and a diagonal matrix D, the float ambiguity solution is transformed into a new coordinate system as shown in the following equation: Based on the decorrelated ambiguity parameters , integer search is performed using least squares criterion to finally determine the fixed integer ambiguity solution : fixed integer ambiguity solution mapping back to the original coordinate system to obtain the final integer ambiguity solution : Re-estimating position change parameters using weighted least squares : 。

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